We present a construction method for mappings between generalized connections, comprising, e.g., the action of gauge transformations, diffeomorphisms and Weyl transformations. Moreover, criteria for continuity and measure preservation are stated.

We study certain bijection between plane partitions and N -matrices. As applications, we prove a Cauchy-type identity for generalized dual Grothendieck polynomials. introduce two statistics on partitions, whose generating functions are similar to classical MacMahon's formulas; one of these is equidistributed with the usual volume. also show natural connections longest increasing subsequences wo...

equality of -curvatures of the berwald and cartan connections leads to a new class of finsler metrics, so-called bc-generalized landsberg metrics. here, we prove that every bc-generalized landsberg metric of scalar flag curvature with dimension greater than two is of constant flag curvature.

In this paper, we first present a new type of the concept of open sets by expressing some properties of arbitrary mappings on a power set. With the generalization of the closure spaces in categorical topology, we introduce the generalized topological spaces and the concept of generalized continuity and become familiar with weak and strong structures for generalized topological spaces. Then, int...

We examine a family of nite energy SO(3) Yang-Mills connections over S 4 , indexed by two real parameters. This family includes both smooth connections (when both parameters are odd integers), and connections with a holonomy singularity around 1 or 2 copies of RP 2. These singular YM connections interpolate between the smooth solutions. Depending on the parameters, the curvature may be self-dua...